기계학습_확률 기초 복습 with python

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

from scipy.stats import binom

# 이항분포 B(n,p)파라미터 설정 
p = 0.3
n = 100

# 이항분포 정의 
dist1 = binom(n,p)

# 이항분포 확률질량함수 dist1.pmf 

Xlist = range(10,50)
Ylist = dist1.pmf(Xlist)
plt.plot(Xlist, Ylist)

# 이항분포의 CDF: dist1.cdf

for n in range(10,100,10):
    print(f'{n}번 이하 성공할 확률:{dist1.cdf(n)*100:0.3f}')

# m:mean (평균), v:variance(분산), s:skewness(왜도), k:kurtosis(첨도)
m,v,s,k = dist1.stats(moments='mvsk')

print(f'X가 B(100,0.3)를 따를 때, 평균:{m}, 분산:{v}, 왜도:{s}, 첨도:{k}')

from scipy.stats import norm

mu = 50 
sigma = 5
dist2 = norm(mu,sigma)

# 정규분포의 확률밀도함수 

Xlist = range(20,80)
Ylist = dist2.pdf(Xlist)
plt.plot(Xlist, Ylist)

dist2.pdf(50)

# 정규분포의 CDF 

print(f'P(40<=X<=60)={dist2.cdf(60)-dist2.cdf(40):5.2f}')

# m:mean (평균), v:variance(분산), s:skewness(왜도), k:kurtosis(첨도)
m,v,s,k = dist2.stats(moments='mvsk')

print(f'X가 N(50,25)를 따를 때, 평균:{m}, 분산:{v}, 왜도:{s}, 첨도:{k}')

from scipy.stats import multivariate_normal

#다변량 정규분포 분산 값 변화에 따른 그래프 모형
x, y = np.mgrid[-1:1:0.01, -1:1:.01]
pos = np.dstack((x, y))

rv1 = multivariate_normal(mean=[0, 0], cov=[[0.1, 0],[0, 0.1]])
rv2 = multivariate_normal(mean=[0, 0], cov=[[1, 0],[0, 1]])

rv3 = multivariate_normal(mean=[0, 0], cov=[[2, 0],[0, 1]])
rv4 = multivariate_normal(mean=[0, 0], cov=[[1, 0],[0, 2]])

rv5 = multivariate_normal(mean=[0, 0], cov=[[1, 0.5],[0.5, 1]])
rv6 = multivariate_normal(mean=[0, 0], cov=[[1, -0.5],[-0.5, 1]])

fig, subplots = plt.subplots(2, 3)
fig.set_figwidth(12)
fig.set_figheight(8)
subplots = subplots.reshape(-1)

subplots[0].contourf(x, y, rv1.pdf(pos), cmap='magma')
subplots[1].contourf(x, y, rv2.pdf(pos), cmap='magma')
subplots[2].contourf(x, y, rv3.pdf(pos), cmap='magma')
subplots[3].contourf(x, y, rv4.pdf(pos), cmap='magma')
subplots[4].contourf(x, y, rv5.pdf(pos), cmap='magma')
subplots[5].contourf(x, y, rv6.pdf(pos), cmap='magma')

subplots[0].set_title('mean=0 cov=[[0.1, 0],[0, 0.1]]')
subplots[1].set_title('mean=0 cov=[[1, 0],[0, 1]]')
subplots[2].set_title('mean=0 cov=[[2, 0],[0, 1]]')
subplots[3].set_title('mean=0 cov=[[1, 0],[0, 2]]')
subplots[4].set_title('mean=0 cov=[[1, 0.5],[0.5, 1]]')
subplots[5].set_title('mean=0 cov=[[1, -0.5],[-0.5, 1]]')